More Waves in Music and Sound

Decibels, Interference and Doppler Effect

Measuring Sound Intensity:Sound "intensity" is measured in Watts, watts/m2 or in Decibels (dB). P0 = 10-12 W/m2 and is the threshold of human hearing. (The lowest amplitude humans can hear)

Wave Addition:

The displacement (maximum displacement is amplitude) of two similar Waves will add for the same location and time.  If two waves are "out of phase" they will cancel each other out with "destructive" interference. 

If two waves are in phase they will have constructive interference. The total amplitude will be the sum of the two waves' amplitude

Destructive Interference

Constructive Interference

If waves have a different wavelength (different frequency) They will add together in the same way, except they will not remain in or out of phase. 

If two notes have similar, but not identical frequencies (or wavelengths) the time in or out of phase will be audible as the tone getting softer and louder (interfering destructivly then constructively) this is called a "beat frequency". The closer the tones are to being the same frequency (or wavelength) the longer the period of the beat frequency, where the beat frequency will be the difference between the two frequencies:

A guitar's "A" playes a tone of 436 Hz, and a tuning fork is played at 440 Hz. The "beat frequency" is 4 Hz.

Doppler Effect

As a sound source moves while producing sound waves, the location of each wave peak is modified by the amount and direction that the source is moving. This will increase the wavelength (decrease the frequency) behind the object and decrease the wavelength (increase the frequency) in front of the object.

λ = original wavelength

λ’ = wavelength in front of moving sound source

λ’ = λ(1-vsource/v) (in front)

λbehind = λ(1+vsource/v)

http://en.wikipedia.org/wiki/Doppler_effect